Abstract

Critically coupled resonant optical cavities are often used as mode cleaners in optical systems to improve the signal-to-noise ratio (SNR) of a signal that is encoded as an amplitude modulation of a laser beam. Achieving the best SNR requires maintaining the alignment of the mode cleaner relative to the laser beam on which the signal is encoded. An automatic alignment system that is primarily sensitive to the carrier field component of the beam will not, in general, provide optimal SNR. We present an approach that modifies traditional dither alignment sensing by applying a large amplitude modulation on the signal field, thereby producing error signals that are sensitive to the signal sideband field alignment. When used in conjunction with alignment actuators, this approach can improve the detected SNR; we demonstrate a factor of 3 improvement in the SNR of a kilometer-scale detector of the Laser Interferometer Gravitational-Wave Observatory. This approach can be generalized to other types of alignment sensors.

© 2011 Optical Society of America

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References

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  1. The LIGO Scientific Collaboration, Rep. Prog. Phys. 72, 076901 (2009).
    [CrossRef]
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2010

H. Grote and The LIGO Scientific Collaboration, Class. Quantum Grav. 27, 084003 (2010).
[CrossRef]

2009

The LIGO Scientific Collaboration, Rep. Prog. Phys. 72, 076901 (2009).
[CrossRef]

2008

The Virgo Collaboration, Class. Quantum Grav. 25, 184001(2008).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef] [PubMed]

2000

1997

G. Breitenbach, S. Schiller, and J. Mlynek, Nature 387, 471(1997).
[CrossRef]

1994

1984

Abbott, R.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Adhikari, R.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Anderson, D. Z.

Breitenbach, G.

G. Breitenbach, S. Schiller, and J. Mlynek, Nature 387, 471(1997).
[CrossRef]

Dooley, K.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Evans, M.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Fricke, T.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Fritschel, P.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Frolov, V.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Grote, H.

H. Grote and The LIGO Scientific Collaboration, Class. Quantum Grav. 27, 084003 (2010).
[CrossRef]

Kawabe, K.

K. Kawabe, N. Mio, and K. Tsubono, Appl. Opt. 33, 5498(1994).
[CrossRef] [PubMed]

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef] [PubMed]

Mavalvala, N.

Mio, N.

Mlynek, J.

G. Breitenbach, S. Schiller, and J. Mlynek, Nature 387, 471(1997).
[CrossRef]

Schiller, S.

G. Breitenbach, S. Schiller, and J. Mlynek, Nature 387, 471(1997).
[CrossRef]

Sigg, D.

Smith-Lefebvre, N.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Tsubono, K.

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef] [PubMed]

Waldman, S.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

Appl. Opt.

Class. Quantum Grav.

The Virgo Collaboration, Class. Quantum Grav. 25, 184001(2008).
[CrossRef]

H. Grote and The LIGO Scientific Collaboration, Class. Quantum Grav. 27, 084003 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Nature

G. Breitenbach, S. Schiller, and J. Mlynek, Nature 387, 471(1997).
[CrossRef]

Rep. Prog. Phys.

The LIGO Scientific Collaboration, Rep. Prog. Phys. 72, 076901 (2009).
[CrossRef]

Science

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef] [PubMed]

Other

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, and S. Waldman, “DC readout experiment in enhanced LIGO,” Class. Quantum Grav., submitted.

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Figures (3)

Fig. 1
Fig. 1

A signal is encoded by interferometry (or any other means) as an amplitude modulation of a laser beam. The beam is then steered by two mirrors that are dithered in angle before passing though a mode cleaner cavity. Alignment signals can be derived by demodulation of the transmitted photocurrent. The misalignment has been grossly exaggerated in the figure.

Fig. 2
Fig. 2

Arrow diagram showing electric fields after transmission through the OMC. In the figure, f d is the angular dither frequency, f b is the beacon modulation frequency.

Fig. 3
Fig. 3

Noise amplitude spectral density (ASD) of the LIGO H1 detector using two types of alignment schemes. The curves are normalized to a calibration line at 1144 Hz . The small line structures are resonances of the suspension wires supporting the mirrors. The beacon scheme shows an SNR improvement of about a factor of 3.

Equations (7)

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SNR c s c 2 + 2 s 2 s .
S standard = P ( f d ) 2 c 2 θ c + 4 s 2 θ s 2 c 2 θ c ,
S beacon = P ( f d + f b ) 2 s c θ c + 2 c s θ s .
S optimal = S beacon P ( f b ) 2 P DC S standard 2 c s θ s + 2 s c θ c 2 c s 2 c 2 ( 2 c 2 θ c ) 2 c s θ s .
SNR = P ( f b ) P DC .
θ ( P ( f b ) P DC ) = 1 P DC ( P ( f b ) θ P ( f b ) 2 P DC P DC θ ) ,
G optimal = G beacon P ( f b ) 2 P DC G standard .

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